The regularization term introduces an optimality gap with respect to worst case perturbations, i.e., \(\mathbb {E}_{g \sim \lambda ^{\star }_c}\left[ \ell (f_{\theta }(g\mathbf {x}), y) \right] \le \max _{g \in \mathcal {G}}\ell \left(f_{\theta }\left(g\mathbf {x}\right), y\right)\) . However, for particular values of \(c\)  the regularized problem has a closed form solution [1]} that allows us to sample from it easily. Namely, there exists a constant \(c \ge 0\)  such that \(\lambda ^{\star }_c(\mathbf {x}, y, g) = \frac{\ell (f_{\theta }(g\mathbf {x}), y)}{c}\) .
